Math Tutor Explains: What is 33 to the Power of 63?

A math tutor would explain that to solve for 33 to the power of 63, we must first understand the structure. The number 33 is called the base, and the number 63 is called the exponent. In short, the base must be multiplied by itself the number of times as the exponent. Let’s look at this problem in more detail.

Math Tutor's Solution: 33 to the Power of 63 is equal to 463850695702570043056734742089693936348147409120368727314339475544679377848802620968225176685537

Methods

Step-by-step from math tutor: finding 33 to the power of 63

The first step a math tutor would suggest is to understand what it means when a number has an exponent. The “power” of a number indicates how many times the base would be multiplied by itself to reach the correct value.

The second step is to write the number in the base-exponent form, and lastly calculate what the final result would be. Consider the example of 2 to the power of 4: in exponent form that would be

242^4
. To solve this, we need to multiply the base, 2 by itself, 4 times -
2⋅2⋅2⋅22\cdot2\cdot2\cdot2
= 16. So
24=162^4 = 16
.

So re-applying these steps to our particular problem, we first convert our word problem to a base-exponent form of:

336333^{63}

To simplify this, all that is needed is to multiply it out:

33 x 33 x 33 x 33 x ... (for a total of 63 times) = 463850695702570043056734742089693936348147409120368727314339475544679377848802620968225176685537

Therefore, 33 to the power of 63 is 463850695702570043056734742089693936348147409120368727314339475544679377848802620968225176685537.

Math Tutor Suggests: Try related exponent problems

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